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  4. ( cot 2 15°-1/ cot 2 15°+1)=

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Q. $\frac{\cot ^2 15^{\circ}-1}{\cot ^2 15^{\circ}+1}=$

TS EAMCET 2021

Solution:

$ \frac{\cot ^2 15-1}{\cot ^2 15+1}=\frac{\cos ^2 15-\sin ^2 15}{\cos ^2 15+\sin ^2 15}=\cos ^2 15-\sin ^2 15$
$ =\cos 15 \cos 15-\sin 15 \sin 15$
$=\cos (15+15)=\cos 30^{\circ}=\frac{\sqrt{3}}{2}$